Back in England in 1801, he was given command of the sloop, ‘’Investigator”, with orders to explore the “Unknown Coast”: that part of southern Australia between what was known from Dutch visits in the west and Flinders’ and Bass's own surveys in the east – basically from the southwest corner of the continent to the site of present-day Melbourne. He did this between December 1801 and May 1802 before proceeding to Port Jackson, (Sydney) In July he continued up the coast, following in the path of James Cook, but more painstakingly, frequently using the ship’s boat close inshore. He surveyed parts of the Great Barrier Reef and the Gulf of Carpentaria, before returning via the already known coasts of the north and west. He had circumnavigated the continent in a leaky, worn out and undersized vessel.

He sailed for England in the schooner, “Cumberland”, calling in at the French island of Mauritius in December 1803, where he was arrested and held as a spy for the next eight years, despite having a passport. He arrived back in England, his health shattered, in 1811, three years before his death in 1814, and the day after the publication of his monumental account: “A Voyage to Terra Australis”, the preface of which includes the words: “Had I permitted myself any innovation upon the original term, it would have been to convert it into Australia; as being more agreeable to the ear, and as an assimilation to the names of the other great portions of the earth.” This is the first recorded use of the name by which the continent, and the nation, would become known.

Flinders was a man of many parts. He is almost unmatched as a surveyor. He is recognised as a fine navigator and seaman, and a considerate and fair commander. His account of his work is acknowledged as that of an intelligent and intellectual man. His experiments with instruments and his study of the science of navigation – especially the effects of wind on a barometer, and the problem of compass irregularities caused by nearby metal, are still applicable today; indeed parts of the modern nautical compass are still named after him.